Question: Simplify to lowest terms. $\dfrac{70}{90}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 90? $70 = 2\cdot5\cdot7$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(70, 90) = 2\cdot5 = 10$ $\dfrac{70}{90} = \dfrac{7 \cdot 10}{ 9\cdot 10}$ $\hphantom{\dfrac{70}{90}} = \dfrac{7}{9} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{70}{90}} = \dfrac{7}{9} \cdot 1$ $\hphantom{\dfrac{70}{90}} = \dfrac{7}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{90}= \dfrac{2\cdot35}{2\cdot45}= \dfrac{2\cdot 5\cdot7}{2\cdot 5\cdot9}= \dfrac{7}{9}$